"Easiest way to do a backup" is a hard thing to define because it depends on your setup, but let me add a few comments that I hope will be helpful.
Running a scheduled archive on the last day of the month depends on the scheduler program that you are using. Most likely you are using TSMs Client Schedule instead of a third party scheduling program (like Maestro, orAutoSys or even cron). Unfortuantly, (as you are probably finding out) TSMs Client Schedule is not the most feature rich scheduler, and it is oriented towards a Weekly (not Monthy) backup cycle.
So what I do is set up a Archive job to start to run on the last weekend (Saturday or Sunday) of the current month then set the Period (PERUnits=) to 1 month.
The other aspects that you need to consider is defining the management class Archive Copy Group to have a retention of 1 month (31 days).
You also need to figure out what the Filespec is going to be for the Archive command. Do you want to backup everything on your Clients? Are there any files you want to exclude from the Archive? Are there multiple drives that you want to Archive? Answering these questions will help you create the Filespec that you will put in the Archive schedule OBJECTS field and in the incl/exclude list.
Sorry for the long post, but you may want to also consider doing monthy Selective backups instead of an archive (but I digress)....